Mathematics
Find the coefficient of x2 and x in the product of (x - 3)(x + 7)(x - 4)
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Answer
We know that (x + a)(x + b)(x + c) = x3 + (a + b + c)x2 + (ab + bc + ca)x + abc
Comparing (x - 3)(x + 7)(x - 4) with (x + a)(x + b)(x + c).
Here a = -3, b = 7, c = -4.
∴ Coefficient of x2 = a + b + c = (-3) + 7 + (-4) = 0 and
coefficient of x = ab + bc + ca
= (-3) x 7 + 7 x (-4) + (-4) x (-3)
= -21 - 28 + 12 = -37
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